Fractal constructs are based on the incorporation of identical motifs that repeat on differing size scales. Examples of fractal shapes in nature include clouds, trees, waves on a lake, the human circulatory system, and mountains, to mention but a few. The study of fractals has moved from the field of pure mathematics, to descriptions of nature that, in turn, inspired artistic design. More recently, chemists have incorporated the fractal form in molecular synthesis. Since 1985, molecular trees, which generally branch in a binary or ternary pattern, have been synthesized with increasing size and structural complexity. Beyond their aesthetics, these dendrimers and hyperbranched materials are now under study for a wide range of practical applications. However, tree-like patterns are but one type of fractal comprised of repeating geometrical figures. A porphyrin-based dendrimer that uses porphyrins as branching centers has been prepared that incorporates the snake-like “Kolam” fractal pattern described by Ascher for example. Nonetheless, most mathematically-defined fractals have yet to be produced in the laboratory.
It would therefore be beneficial to provide the chemical synthesis of fractal constructs, such as non-dendritic fractal constructs, based on Sierpinski's hexagonal gasket (incorporating both the Star of David and a Koch snowflake) where the terminology ‘non-dendritic’ refers to repeat units that do not branch in the typical tree-like pattern.